Question

A concave mirror of focal length 12 cm forms three times the magnified virtual image of an object. Find the distance of the object from the mirror.

Answer 1

Given Data:

• Focal length (f) = −12 cm (Concave mirror → Focal length is negative)
• Magnification (m) = +3 (Virtual, magnified image → Positive magnification)
• Object distance (u) = ?

Use Magnification Formula

${\displaystyle m=-\frac{v}{u}}$

${\displaystyle 3=-\frac{v}{u}}$

v = −3u

${\displaystyle \frac{1}{f}=\frac{1}{v}+\frac{1}{u}}$

Substituting f = −12 and v = −3u:

${\displaystyle \frac{1}{-12}=\frac{1}{-3u}+\frac{1}{u}}$

${\displaystyle \frac{1}{-12}=\frac{1+3}{3u}}$

${\displaystyle \frac{1}{-12}=\frac{4}{3u}}$

−12 × 4 = 3u

−48 = 3u

u = −8 cm

The negative sign indicates that the object is placed in front of the mirror at a distance of 8 cm from the pole.